In gay slang, a “friend of Dorothy” (occasionally abbreviated FOD) is a gay man. The phrase dates back to at least World War II, when homosexual acts were illegal in the United States. Stating that, or asking if, someone was a “friend of Dorothy” was a euphemism used for discussing sexual orientation without others knowing its meaning. A similar term, “friend of Mrs. King” (i.e. Queen, in the meaning of ‘gay man’) was used in England, mostly in the first half of the 20th century.
In the early 1980s, the Naval Investigative Service was investigating homosexuality in the Chicago area. Agents discovered that gay men sometimes referred to themselves as “friends of Dorothy”. Unaware of the historical meaning of the term, the NIS believed that there actually was a woman named Dorothy at the center of a massive ring of homosexual military personnel, so they launched an enormous and futile hunt for the elusive “Dorothy”, hoping to find her and convince her to reveal the names of gay service members.
Starting in the late 1980s, on several cruise lines, gay and lesbian passengers began approaching ship staff, asking them to publicise gatherings in the daily cruise activity list. As the cruise lines were hesitant to announce such things so blatantly in their daily publications, they would list the gathering as a “Meeting of the Friends of Dorothy”. The use of this phrase likely comes from the cruise directors who were also familiar with and using the “Friends of Bill W.” phrase in their programs to tell members of Alcoholics Anonymous that there were support group meetings on the trip.